// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Eigenvalues>

template<typename Scalar, int Size>
void
hessenberg(int size = Size)
{
	typedef Matrix<Scalar, Size, Size> MatrixType;

	// Test basic functionality: A = U H U* and H is Hessenberg
	for (int counter = 0; counter < g_repeat; ++counter) {
		MatrixType m = MatrixType::Random(size, size);
		HessenbergDecomposition<MatrixType> hess(m);
		MatrixType Q = hess.matrixQ();
		MatrixType H = hess.matrixH();
		VERIFY_IS_APPROX(m, Q * H * Q.adjoint());
		for (int row = 2; row < size; ++row) {
			for (int col = 0; col < row - 1; ++col) {
				VERIFY(H(row, col) == (typename MatrixType::Scalar)0);
			}
		}
	}

	// Test whether compute() and constructor returns same result
	MatrixType A = MatrixType::Random(size, size);
	HessenbergDecomposition<MatrixType> cs1;
	cs1.compute(A);
	HessenbergDecomposition<MatrixType> cs2(A);
	VERIFY_IS_EQUAL(cs1.matrixH().eval(), cs2.matrixH().eval());
	MatrixType cs1Q = cs1.matrixQ();
	MatrixType cs2Q = cs2.matrixQ();
	VERIFY_IS_EQUAL(cs1Q, cs2Q);

	// Test assertions for when used uninitialized
	HessenbergDecomposition<MatrixType> hessUninitialized;
	VERIFY_RAISES_ASSERT(hessUninitialized.matrixH());
	VERIFY_RAISES_ASSERT(hessUninitialized.matrixQ());
	VERIFY_RAISES_ASSERT(hessUninitialized.householderCoefficients());
	VERIFY_RAISES_ASSERT(hessUninitialized.packedMatrix());

	// TODO: Add tests for packedMatrix() and householderCoefficients()
}

EIGEN_DECLARE_TEST(hessenberg)
{
	CALL_SUBTEST_1((hessenberg<std::complex<double>, 1>()));
	CALL_SUBTEST_2((hessenberg<std::complex<double>, 2>()));
	CALL_SUBTEST_3((hessenberg<std::complex<float>, 4>()));
	CALL_SUBTEST_4((hessenberg<float, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
	CALL_SUBTEST_5((hessenberg<std::complex<double>, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));

	// Test problem size constructors
	CALL_SUBTEST_6(HessenbergDecomposition<MatrixXf>(10));
}
